Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2011
• Hauptverfasser: Deguchi, T., Sato, J.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут математики НАН України 2011
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/147175
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Quantum Group Uq(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain / T. Deguchi, J. Sato // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 73 назв. — англ.

We show some symmetry relations among the correlation functions of the integrable higher-spin XXX and XXZ spin chains, where we explicitly evaluate the multiple integrals representing the one-point functions in the spin-1 case. We review the multiple-integral representations of correlation functions for the integrable higher-spin XXZ chains derived in a region of the massless regime including the anti-ferromagnetic point. Here we make use of the gauge transformations between the symmetric and asymmetric R-matrices, which correspond to the principal and homogeneous gradings, respectively, and we send the inhomogeneous parameters to the set of complete 2s-strings. We also give a numerical support for the analytical expression of the one-point functions in the spin-1 case.